Numerical comparison of a constrained path ensemble and a driven quasisteady state

Abstract

We investigate the correspondence between a non-equilibrium ensemble defined via the distribution of phase-space paths of a Hamiltonian system, and a system driven into a steady-state by non-equilibrium boundary conditions. To discover whether the non-equilibrium path ensemble adequately describes the physics of a driven system, we measure transition rates in a simple one-dimensional model of rotors with Newtonian dynamics and purely conservative interactions. We compare those rates with known properties of the non-equilibrium path ensemble. In doing so, we establish effective protocols for the analysis of transition rates in non-equilibrium quasi-steady states. Transition rates between potential wells and also between phase-space elements are studied, and found to exhibit distinct properties, the more coarse-grained potential wells being effectively further from equilibrium. In all cases the results from the boundary-driven system are close to the path-ensemble predictions, but the question of equivalence of the two remains open.